86 lines
2.5 KiB
C
86 lines
2.5 KiB
C
/* inv_div_qr_n - quotient and remainder using a precomputed inverse
|
|
|
|
Copyright 2010 William Hart
|
|
|
|
This file is part of the MPIR Library.
|
|
|
|
The MPIR Library is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU Lesser General Public License as published by
|
|
the Free Software Foundation; either version 2.1 of the License, or (at your
|
|
option) any later version.
|
|
|
|
The MPIR Library is distributed in the hope that it will be useful, but
|
|
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
|
|
License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public License
|
|
along with the MPIR Library; see the file COPYING.LIB. If not, write to
|
|
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
|
|
MA 02110-1301, USA. */
|
|
|
|
#include <mpir.h>
|
|
#include "gmp-impl.h"
|
|
#include "longlong.h"
|
|
|
|
/*
|
|
Computes the quotient and remainder of { np, 2*dn } by { dp, dn }.
|
|
We require dp to be normalised and inv to be a precomputed inverse
|
|
of { dp, dn } given by mpn_invert.
|
|
*/
|
|
mp_limb_t
|
|
mpn_inv_div_qr_n(mp_ptr qp, mp_ptr np,
|
|
mp_srcptr dp, mp_size_t dn, mp_srcptr inv)
|
|
{
|
|
mp_limb_t cy, lo, ret = 0;
|
|
mp_ptr tp;
|
|
TMP_DECL;
|
|
|
|
TMP_MARK;
|
|
|
|
if (mpn_cmp(np + dn, dp, dn) >= 0)
|
|
{
|
|
ret = 1;
|
|
mpn_sub_n(np + dn, np + dn, dp, dn);
|
|
}
|
|
|
|
tp = TMP_ALLOC_LIMBS(2*dn + 1);
|
|
mpn_mul(tp, np + dn - 1, dn + 1, inv, dn);
|
|
add_ssaaaa(cy, lo, 0, np[dn - 1], 0, tp[dn]);
|
|
ret += mpn_add_n(qp, tp + dn + 1, np + dn, dn);
|
|
ret += mpn_add_1(qp, qp, dn, cy);
|
|
|
|
/*
|
|
Let X = B^dn + inv, D = { dp, dn }, N = { np, 2*dn }, then
|
|
DX < B^{2*dn} <= D(X+1), thus
|
|
Let N' = { np + n - 1, n + 1 }
|
|
N'X/B^{dn+1} < B^{dn-1}N'/D <= N'X/B^{dn+1} + N'/B^{dn+1} < N'X/B^{dn+1} + 1
|
|
N'X/B^{dn+1} < N/D <= < N'X/B^{dn+1} + 1 + 2/B
|
|
There is either one integer in this range, or two. However, in the latter case
|
|
the left hand bound is either an integer or < 2/B below one.
|
|
*/
|
|
|
|
if (UNLIKELY(ret == 2))
|
|
{
|
|
ret = 1;
|
|
mpn_sub_1(qp, qp, dn, 1);
|
|
}
|
|
|
|
/* Special case, multiply out to get accurate quotient */
|
|
ret -= mpn_sub_1(qp, qp, dn, 1); /* ret is now guaranteed to be 0 */
|
|
mpn_mul_n(tp, qp, dp, dn);
|
|
mpn_sub_n(np, np, tp, 2*dn);
|
|
while (np[dn] || mpn_cmp(np, dp, dn) >= 0)
|
|
{
|
|
ret += mpn_add_1(qp, qp, dn, 1);
|
|
np[dn] -= mpn_sub_n(np, np, dp, dn);
|
|
}
|
|
|
|
/* Not possible for ret == 2 as we have qp*dp <= np */
|
|
|
|
TMP_FREE;
|
|
|
|
return ret;
|
|
}
|
|
|